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Simplifying 5x2 + -8 + -15x2 + 11 + 3x = 0 Reorder the terms: -8 + 11 + 3x + 5x2 + -15x2 = 0 Combine like terms: -8 + 11 = 3 3 + 3x + 5x2 + -15x2 = 0 Combine like terms: 5x2 + -15x2 = -10x2 3 + 3x + -10x2 = 0 Solving 3 + 3x + -10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.3x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.3x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.3x + x2 = 0.0 + 0.3 -0.3x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -0.3x + x2 = 0.3 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 0.3 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.3 + 0.0225 Combine like terms: 0.3 + 0.0225 = 0.3225 0.0225 + -0.3x + x2 = 0.3225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.3225 Calculate the square root of the right side: 0.567890835 Break this problem into two subproblems by setting (x + -0.15) equal to 0.567890835 and -0.567890835.Subproblem 1
x + -0.15 = 0.567890835 Simplifying x + -0.15 = 0.567890835 Reorder the terms: -0.15 + x = 0.567890835 Solving -0.15 + x = 0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.567890835 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.567890835 + 0.15 x = 0.567890835 + 0.15 Combine like terms: 0.567890835 + 0.15 = 0.717890835 x = 0.717890835 Simplifying x = 0.717890835Subproblem 2
x + -0.15 = -0.567890835 Simplifying x + -0.15 = -0.567890835 Reorder the terms: -0.15 + x = -0.567890835 Solving -0.15 + x = -0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.567890835 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.567890835 + 0.15 x = -0.567890835 + 0.15 Combine like terms: -0.567890835 + 0.15 = -0.417890835 x = -0.417890835 Simplifying x = -0.417890835Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.717890835, -0.417890835}
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